I'm use SQL Prompt v6.2, and quite often I have an issue were SQL Prompt & Intellisense both pop-up at the same time and interfere with each other (see image below).

In previous versions, I would set the delay to 400ms, which would allow Intellisense to pop-up for simple things, e.g. column or table names. However, if Intellisense couldn't find what I needed in time, SQL Prompt came to the rescue.

Prompt should have disabled the built in intellisense on install, was this not the case for you?
To disable the built in intellisense you can navigate to Tools->Options->Text Editor->Transact-SQL and then untick Auto list members and Parameter Information.

If you want both, could I ask what advantages you find with having both enabled? (maybe there's something we could change in Prompt to make it cover those cases?)